What Is the Kinetic Energy of the Bigger Mass After an Explosion?

[Victorzaroni]

Homework Statement

An explosive of mass M is initially at rest. It then explodes into two pieces and travels along a straight line. The small piece has mass M₁, speed V₁, and kinetic energy K₁=(1/2)M₁V₁². The kinetic energy of the bigger mass would be in terms of K₁ would be:

Homework Equations

K=(1/2)mv²

The Attempt at a Solution

I'm not sure how to proceed without a mass ratio. The answer is [M₁/(M-M₁)]K₁

 

[phyzguy]

If an object of mass M splits into two pieces, one of which has mass M1, then what is the mass of the other one? Doesn't this give you a mass ratio?

 

[Victorzaroni]

If an object of mass M splits into two pieces, one of which has mass M1, then what is the mass of the other one? Doesn't this give you a mass ratio?

Yes I figured that part out. So M-M1 is the mass of the other piece. I don't know how to factor this into an equation that relates the kinetic energy of the first piece.

 

[Victorzaroni]

Oh I think I understand why the answer is the answer. Dividing the small mass by the big mass gives you the ratio, and then multiplying this by the small pieces Kinetic Energy gives you the fraction of kinetic energy that the big piece has. I think. Now how do I put that in equation form to show that?

 

[phyzguy]

First you need to conserve momentum. Since the object is initially at rest, it has zero momentum. Since momentum is conserved, it still has zero total momentum after the explosion. Since you know the momentum of one piece, what is the momentum of the other piece? Once you've calculated its momentum, since you know its mass, you can calculate its velocity and then its kinetic energy.